prof. Cornelia Schiebold: An operator theoretic approach to soliton equations and noncommutative integrable systems.

Abstract:

Our point of departure is an operator theoretic approach to soliton equations, which is inspired by work of Marchenkov and enables us Banach geometry in the study of solution families. As a motivation, we will explain this for the classical KdV equation. Then we will discuss further developments of the method in the study of matrix equations and hierarchies. In the applications part, we will talk on the asymptotic description of multiple pole solutions, on the construction of solutions to matrix equations and countable nonlinear superposition.